automotive pressure sensor calibration

Pressure sensors are widely used in automotive systems. In this article we present a brief
description of the architecture of pressure sensors. We also
describe a calibration process for pressure sensors that use mixed-signal integrated circuits as signal conditioners.

Background

From an electrical/electronics engineering perspective, a passenger
car is an aggregation of various control systems that interact with
each other in complex ways. Each control system is made up of a
plant, sensors, actuators and an electronic control unit (ECU).
Figure 1 shows a block diagram representation of an automotive
control system.

Figure 1: Block
diagram representation of an automotive control system.

The ECU is typically a printed circuit board (PCB) with many
circuits. These circuits include passive components such as
resistors, capacitors, inductors, varistors, and integrated circuits
(ICs) such as microcontrollers, regulators, communication
transceivers, transistors and so on. The microcontroller in an ECU
has non-volatile memory that is used to store control algorithms.
The microcontroller also has computation engines to execute the
control algorithms and thereby achieve the intended plant behavior.

One of the important aspects of automotive control systems is the
sensor. The sensor is used to convert the physical entity of
interest into an electrical quantity so that the ECU can use it to
perform control actions.

A typical sensor
in automotive applications has two building blocks (Figure 2):

1. sense element
2. signal conditioner

Figure 2: Block
diagram representation of a typical sensor.

Sense element

The primary purpose of the sense element (SE) is to convert the
physical quantity into electrical signal, typically voltage.

The majority of automotive pressure sense elements are based on
resistors or capacitors. In resistor-based pressure sensors,
resistors are implanted on a flexible diaphragm that flexes with
pressure. In the case of capacitive-based pressure sensors, the
flexible diaphragm that flexes with pressure has a metal plate that
is one electrode of a capacitor.

The sense element undergoes a change in its value (either change in
resistance or change in capacitance) as the pressure changes. The
pressure can be inferred by measuring this electrical value.

With regard to pressure sensors based on resistive-bridge, the
resistors that change in value typically are arranged in bridge
configuration. Figure 3 shows full Wheatstone bridge arrangement of
the resistors. As the pressure changes, the value of resistance in
each bridge leg changes. This in turn causes the output of the
Wheatstone bridge to change.

Figure 3:
Resistors arranged in Wheatstone bridge configuration to form the
pressure sensor.

Note that the resistance itself changes either because the length of
each resistor changes as the diaphragm flexes, which is a strain
gauge effect, or because of change in resistivity of the resistor as
the diaphragm flexes, known as a piezoelectric effect. Furthermore,
in both strain gauge and piezoelectric effects, the resistances
change linearly with pressure. This is because the resistance is
given by Equation 1:

Ideal sense element

In an ideal SE, the output of the bridge is given by Equation 2:

From Equation 2, one can infer that the output of the Wheatstone
bridge changes linearly with resistance. Furthermore, since each
resistor value changes linearly with pressure, one can infer that
the Wheatstone bridge output changes linearly with pressure.

Non-ideal sense element

The bridge output, however, suffers from non-idealities. Figure 4
shows the non-idealities exhibited by the Wheatstone bridge output
as the pressure changes. The non-idealities are a result of
mismatches in the resistor value in each leg, as well as mismatches
in resistor value change with pressure. These individual mismatches
result in the output to exhibit a non-ideal macro behavior.

Figure 4.
Pressure sense element output.

Figure 4, which shows the variation of the bridge output with
pressure, shows the following specific non-idealities:

Because manufacturing tolerances of the resistors vary, each sense
element has a unique non-ideality. In other words, each sense
element has a unique relationship between the pressure and its
output, making it difficult to infer fluid pressure from the bridge
output.

Signal conditioner

The primary purpose of the signal conditioner (SC) is to process the
output of the sense element for its non-idealities and provide the
processed output to the ECU.

One way to eliminate the non-idealities is to precision trim the
resistors so that all the resistors are well-matched. However, this
is usually an expensive process. An alternative to
precision-trimming is to employ a signal conditioner to eliminate
the non-idealities of the SE.

The block diagram in Figure 5 represents a sense element signal
conditioner for Wheatstone bridge. The signal conditioner receives
power from the outside world. The regulators are used to generate
the bridge supply as well as supplies for various circuits in the
signal conditioner. The analog front-end (AFE) is the “first”
interface to the sense element output. The compensation block
eliminates the non-idealities exhibited by the sense element. The
compensated output is then sent to the outside world using the
output block. The output forms could be analog or digital
output, such as LIN and SENT protocol. Automotive pressure sense
element signal conditioners also include other functions such as
diagnostics. The diagnostics block detects faults in either the
sense element or the signal conditioner.

The signal conditioner can be built using discrete electronic
components or comes in the form of highly integrated circuits such
as Texas Instruments’ PGA400, which has a mixed-signal
architecture non-idealities are corrected primarily in the digital
domain.

Removing the Non-Idealities

In mixed-signal conditioners, compensation is accomplished primarily
in the digital domain. To perform compensation in the digital
domain, mixed-signal devices employ analog-to-digital converters
(ADC) to digitize the analog output of the Wheatstone bridge. In
these devices, the principal purpose of the AFE is to scale the
Wheatstone bridge’s output to fit into the ADC’s dynamic input
range.

Analog front-end

Consider, for example, that the Wheatstone bridge varies from VMIN
to VMAX while the ADC dynamic range is AMIN to AMAX. The bridge
output can be scaled to fit into the ADC dynamic range using the
scaling Equation 3:

In other words, the output of the AFE (which is the input to the
ADC) can be expressed using Equation 4:

From Equation 4, one can infer that the scaling is accomplished by
the AFE using a gain and an offset. The gain and offset values in
the AFE are implemented as programmable values to account for
variable offsets and bridge output spans. The variable offsets and
gains are implemented in discrete steps. Even though Equation 2
gives the ideal scaling, AFE output is given by Equation 5:

The result of these discrete steps in gain and offset is that the
bridge output cannot be exactly scaled to fit into the entire
dynamic range of the ADC input. The minimum bridge output is scaled
to A’MIN, which is greater than AMIN, while the maximum bridge
output is scaled to A’MAX, which is less than AMAX. Figure 6
summarizes the scaling process.

Figure 6: The
AFE scales the sense element output to fit into the ADC dynamic
range.

Compensation

The compensation for the sense element output is the process of
eliminating the non-idealities exhibited by the sense element. The
compensation in the digital domain is achieved using nonlinear
equations. One example of a nonlinear equation is given in Equation
6:

Compensation equations can take any form similar to Equation 6. For
instance, TI’s PGA400 offers customers the flexibility to implement
a compensation equation that is appropriate for their sense element.

Calibration

Having chosen a compensation equation, the various coefficients in
the compensation equation have to be determined. However,
before one can do this, the AFE gain and offset also need to be
determined. That is, the calibration process needs to determine two
sets of unknown variables:

Figure 7 shows a high-level flow chart for pressure sensor
calibration using mixed-signal conditioners. This flow-chart
illustrates that the calibration is a two-step process. The first
step is determines the AFE scaling factors and the second step
determines the digital equation coefficients.

Figure 7:
The calibration using mixed-signal devices is a two-step process.

Determining the unknown variables requires appropriate calibration
equipment in the production line, which also involves time on the
production line. In other words, the calibration of every sense
element involves cost. This cost is proportional to the time spent
in the calibration process. Hence, the calibration process involves
a tradeoff between the number of unknown coefficients, which
directly translates the end-accuracy of the pressure sensor, and the
time spent in the calibration process, which translates to cost. Or,
the higher the accuracy desired, the more costly the calibration
process may become.

Note that the calibration is performed after the sense element is
connected to the signal conditioner.

Analog front-end calibration

The AFE calibration is usually an online process. That is, the gain
and the offset in the AFE are adjusted while the sense element is
exposed to certain pressure and temperature conditions (Figure 8).
The sense element is first exposed to a temperature T1 and pressure
P1, or the minimum pressure that the sense element has to measure.
The AFE offset is then adjusted so that the AFE output is as close
as possible to the minimum ADC input value. The pressure is then
changed to P2, which is the maximum pressure that the sense element
has to measure. At the maximum pressure value, the gain is adjusted
so that the AFE output is as close as possible to the maximum ADC
input value. For this method to be valid, it is assumed that the
offset scales with the AFE gain, which is the case with the PGA400.

Figure 8: AFE
calibration.

Digital coefficient calibration

Once the AFE is calibrated, one can determine the digital
coefficients. Determining the actual digital coefficients is an
“offline” process. For instance, the sense element is exposed to
different temperature and pressure conditions and the ADC outputs
are recorded. The recorded ADC values are then used to compute the
digital coefficients offline.

Figure 9 summarizes the digital coefficient calibration process. The
number of temperature and pressure set points at which the digital
representation of temperature and the bridge output are recorded
typically depends on the number of coefficients.

Figure 9:
Digital coefficient calibration.

Calculating digital coefficients

Consider the compensation equation given by Equation 6. This
compensation equation consists of five coefficients. Hence the
temperature and the pressure ADC values are recorded at five unique
temperature and pressure point.

If the desired value at the ith set point is yi, i=1, 2, 3, 4, 5,
then the matrix given by Equation 7 can be constructed as:

The unknown coefficients can be computed using the matrix inversion
formula given by Equation 8:
Eq. 8

Standard tools such as Microsoft™ Excel or Mathworks®
Matlab® can be used to calculate the unknown coefficient values.

Arun Tej Vemuri is a systems engineer with TI’s Kilby Labs. Prior to joining Kilby Labs, Arun
was part of TI’s mixed-signal Automotive group where he was
responsible for product definition of automotive sensor signal
conditioners. Arun received his Ph.D. in Electrical Engineering
from the University of Cincinnati, Ohio, his MS in Systems Science
from IISc Bangalore, India, and BSEE in Electrical Engineering
from IIT Roorkee, India. Arun can be reached at
ti_arunvemuri@list.ti.com.